9.5 SERIES
You never know when you might need math…
FINITE SERIESThere is an end number.
FINITE SERIESSUMMATION NOTATION
Number you go to
Index of summation (Number you start with)
EXAMPLES:
k1 k2 k3 k4 k5 k6
7
k4 k5 k6 k7
k2 k3 k4 k5
EXAMPLES:
EXAMPLES:k
FINITE ARITHMETIC
n=# of terms =1st term = last term
n=# of terms =1st termd=common difference
EXAMPLES:-7,-3,1,5,9,13
117, 110,103…33
=-7 =13n=6
117-3384/7=d 13 terms
FINITE GEOMETRIC
n=# of terms =1st term r= ratio
EXAMPLES:
=5r=3n=10
98415/3=32805
5,15,45…98415
INFINITE SERIESThere is no end.
INFINITE SERIESSUMMATION NOTATION
Goes to infinity (Never ends)
Index of summation (Number you start with)
GEOMETRIC
Converge=sumDiverge=no sum
Converge if |r|<1Not converge, sum=
EXAMPLES:
a r
6+3+3/2+3/4…Mult. By ½=r
4-2+1-1/2+1/4…r=-1/2
EXAMPLES:A ball is dropped at 5 feet. It rebounds to 80% of the last bounce. What is the total distance?
a=5r=.8
WORKS CITED Demana, Franklin, Bert K. Waits,
Gregory D. Foley, and Daniel Kennedy. Graphing Calculator Manual ; Precalculus, Graphical, Numerical, Algebraic :. Boston, MA: Pearson Addison Wesley, 2007. Print.
Krzykowski, Kylee. Notebook; Precalculus with Barber. Lincoln, H.S. 2013. Print.